Toshiaki Shoji

collaborators

3 papers

math.QA2026

Monomial bases and canonical bases for quantum affine algebras

Toshiaki Shoji, Zhiping Zhou

We construct a monomial basis of a quantum affine algebra of simply-laced type, associated to the PBW basis of Beck-Nakajima. We show that there exists a simple algorithm of comput…

math.QA2025

Algorithm for computing canonical bases and foldings of quantum groups

Toshiaki Shoji, Zhiping Zhou

Let $U_{q}^{-}$ be the negative half of a quantum group of finite type. Let $P$ be the transition matrix between the canonical basis and a PBW basis of $U_{q}^{-}$ . In…

math.QA2025

Elementary construction of canonical bases, foldings, and piecewise linear bijections

Toshiaki Shoji, Zhiping Zhou

Let $U_{q}^{-}$ be the negative half of a quantum group of finite type. We construct the canonical basis of $U_{q}^{-}$ by applying the folding theory of quantum groups…